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the other hand, if we are given a principal bundle, then the "solder forms" are not canonical, but once they are given they allow us to uniquely identify this principal bundle with a bundle of frames so that the solder forms correspond to the restriction of the canonical forms. Thus, the solder forms allow us to "solder" (in the sense of "identify") the two bundles.
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the other hand, if the term is indeed used this way in some circles (i.e. for a vector-valued form on FM), then the distinction should be made crystal clear. Otherwise, the language will be very confusing to nonexperts (such as myself). I chose not to delete it myself, but, as it stands, this piece of the article is very confusing.
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have also been called "canonical" or "solder" forms. The terminology depends on the context. When we are given the frame bundle of a manifold, the correct terminology is "fundamental" or "canonical" forms since, as described in the definition, they are canonically determined on the frame bundle. On
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The term "tautological/fundamental" 1-form is almost universally employed in reference to the form on T^*M, not FM --- including in the wikipedia article on the subject. If your use of the term in the context of FM is homegrown, it should be done away with entirely in the interest of clarity. On
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This is a reasonable point, although I would then say that the frame bundle therefore has a canonical (or tautological) solder form. Anyway, I don't feel strongly about it (although I think "canonical" and "tautological" are a bit more descriptive than "fundamental"), so do as you think best.
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husemoller talks about orthonormal k-frames a bit differently, and there does not seem to be an article talking about that, should it be mentioned here or should we at least point towards the stiefel variety/manifold?-sean, a lowly math student.
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to be honest. The discussion of bundle maps is far too short, and definitely needs to be fleshed out with a diagram. But diagrams are a good thing in general, so why not put one here too.
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170:"vierbein" refers to frames in four dimensions, "vielbein" refers to frames in many dimensions: the German for four is "vier" and for many is "viel". I hope that helps!
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should these frames not be orthonormal? or does it not matter since you can untwist the fibre locally?
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I've realized the spelling "vielbein" is far more common than "vierbein".
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